As you already have one Adsense in your hand, you can associate the particular Adsense to more than hundreds of sites.
There is no need to have other Adsense for your personal blog.
Moreover, Google allows only one Adsense per IP Address. Even If you apply for Adsense with whatever information, you will not get the approval in anyways since Google monitors each and every IP for their security check.
Afterwards your original account which you presently have will also be under a bit of a trouble from Google, since they would believe that you are under the mode of creating multiple accounts with Adsense and trying to fool them around.
We advise you not to go anywhere else, but use your very own Adsense which you have.